from some other cause than refraction.  And thirdly, I cannot conceive how these motions should not happen sometimes to oppose each other, and then, in stead of a rotation, there would be nothing but a direct motion generated, and consequently no colour.  And fourthly, I cannot conceive, how by the Cartesian Hypothesis it is possible to give any plausible reason of the nature of the Colours generated in the thin laminae of these our Microscopical Observations; for in many of these, the refracting and reflecting surfaces are parallel to each other, and consequently no rotation can be generated, nor is there any necessity of a shadow or termination of the bright Rays, such as is suppos’d (Chap. 8.  Sec. 5. Et praeterea observavi umbram quoque, aut limitationem luminis requiri: and Chap. 8.  Sec. 9.) to be necessary to the generation of any distinct colours; Besides that, here is oftentimes one colour generated without any of the other appendant ones, which cannot be by the Cartesian Hypothesis.

There must be therefore some other propriety of refraction that causes colour.  And upon the examination of the thing, I cannot conceive any one more general, inseparable, and sufficient, than that which I have before assign’d.  That we may therefore see how exactly our Hypothesis agrees also with the Phaenomena of the refracting round body, whether Globe or Cylinder, we shall next subjoyn our Calculation or Examen of it.

And to this end, we will calculate any two Rays:  as for instance;[10] let EF be a Ray cutting the Radius CD (divided into 20. parts) in G 16. parts distant from C, and ef another Ray, which cuts the same Radius in g 17. parts distant, these will be refracted to K and k, and from thence reflected to N and n, and from thence refracted toward P and p; therefore the Arch Ff will be 5.d 5’.  The Arch FK 106.d 30’. the Arch fk 101.d 2’.  The line FG 6000. and fg 5267. therefore hf. 733. therefore Fc 980, almost.  The line FK 16024. and fk 15436. therefore Nd 196. and no 147 almost, the line Nn 1019 the Arch Nn 5.d 51’. therefore the Angle Nno is 34.d 43’. therefore the Angle Non is 139.d 56’. which is almost 50.d more than a right Angle.

It is evident therefore by this Hypothesis, that at the same time that ef touches f.  EF is arrived at c.  And by that time efkn is got to n, EFKN is got to d and when it touches N, the pulse of the other Ray is got to o. and no farther, which is very short of the place it should have arriv’d to, to make the Ray np to cut the orbicular pulse No at right Angles:  therefore the Angle Nop is an acute Angle, but the quite contrary of this will happen, if 17. and 18. be calculated in stead of 16. and 17. both which does most exactly agree with the Phaenomena:  For if the Sun, or a Candle (which is better) be placed about Ee, and the eye about Pp, the Rays EFef at 16. and 17. will paint the side